Pile of $2000$ cards

Question

A pile of cards $2000$ is labeled with integers from $1$ to $2000$, with different integers of different cards. The cards in the pile are not in numerical order. The top card is removed from the pile and placed on a table, and the second on the pile is moved under the pile. The new top card is removed from the top to the table, for the right of the first one, and the next on the pile is moved under the pile. This process - putting the card from top of the pile at right of the cards placed on the table and move the next card from the pile to below - is repeated until all cards are on the table. At the end it was observed that, reading from left to right, the cards were in the following order: $1, 2, 3, \dots, 1999, 2000$. In the original pile, how many cards there were above the card $1999$?

Answer 1

Hint: where did card 1 start out? card 2? card 3? After the first pass through the deck, how many cards are on the table? which ones are they? where were the ones that are still in the pile? How does this relate to the Josephus problem?